Question

consider \\(8^{x-4} = 8^{10}\\)

because the dropdown are equal, the dropdown must also be equal.

Explanation:

Identify the components of the exponential equation

Using the Solving Exponential Equations Algebraically knowledge point

$$ 8^{x-4} = 8^{10} $$

The base on both sides of the equation is \(8\). The exponent on the left side is \(x-4\), and the exponent on the right side is \(10\).

Apply the property of equality for exponential functions

Using the Solving Exponential Equations Algebraically knowledge point

$$ \text{If } b^y = b^z \text{ and } b > 0, b eq 1, \text{ then } y = z. $$

Because the bases are equal, the exponents must also be equal.

Answer:

Consider \(8^{x-4} = 8^{10}\)

Because the <blank>bases</blank> are equal, the <blank>exponents</blank> must also be equal.